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#173easyOptions & Derivatives

Put Price from Parity

Part of:Options & Derivatives → Put-Call Parity & Payoffs

Problem

Given the price of a European call option, compute the price of the corresponding European put option using put-call parity.

Given:

  • C — European call price
  • S — current spot price
  • K — strike price
  • T — time to expiry (years)
  • r — continuously compounded risk-free rate

Put-Call Parity

C−P=S−Ke−rTC - P = S - K e^{-rT}

Rearranging:

P=C−S+Ke−rTP = C - S + K e^{-rT}

Input Format

Five space-separated floats: C S K T r

Output Format

The European put price rounded to 4 decimal places.

Examples

Example 1
Input(Five space-separated floats: C S K T r)
10.4506 100.0 100.0 1.0 0.05
Output
5.5735

ATM option: C=10.4506, S=K=100, T=1, r=5% -> P=5.5735.

Example 2
Input(Five space-separated floats: C S K T r)
3.8986 100.0 110.0 0.5 0.03
Output
12.2609

OTM call / ITM put: the put is more expensive.

Constraints

  • •0.0 <= C <= 100000.0
  • •1.0 <= S <= 10000.0
  • •1.0 <= K <= 10000.0
  • •0.01 <= T <= 10.0
  • •0.0 <= r <= 0.5
  • •Output put price to 4 decimal places

Execution limits: 2s · 256MB

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